Question: $A$ $B$ $C$ If: $ AC = 37$, $ BC = 5x + 5$, and $ AB = 3x + 8$, Find $BC$.
Answer: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {3x + 8} + {5x + 5} = {37}$ Combine like terms: $ 8x + 13 = {37}$ Subtract $13$ from both sides: $ 8x = 24$ Divide both sides by $8$ to find $x$ $ x = 3$ Substitute $3$ for $x$ in the expression that was given for $BC$ $ BC = 5({3}) + 5$ Simplify: $ {BC = 15 + 5}$ Simplify to find ${BC}$ : $ {BC = 20}$